math errors

food_energy.tex

@@ -56,14 +56,14 @@ A proto-college-student at Winona's China King Buffet, dreaming about visiting t
 \end{figure}
 
 \subsection{Converting food into body heat}
-Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am, eg figure \ref{buffet}.  If he brings homework and stretches the meal out for a few hours he can get all $3000kcals$ with only one meal bill.  Food is fuel for the human body -- could too much fuel make his body feel sick? If his body burned all this food at once, how much warmer would he get? 
+Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am, eg figure \ref{buffet}.  If he brings homework and stretches the meal out for a few hours he can get all $3000kcals$ with only one bill.  Food is fuel for the human body -- could too much fuel make his body feel sick? If his body burned all this food at once, how much warmer would he get? 
 Useful information: the student has a mass of $80kg$ and is made mostly of water.  A Calorie heats $1 kg$ of water $1^{\circ}C$. 
 
 Here's a possible answer:
 equate food energy with calorimetric heating and assume human bodies have the same heat capacity as water, about $1\frac{kcal}{kg\cdot\degC}$. This allows us to calculate the body's temperature increase.
 \bea
-3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot \degC}\cdot\Delta T\\
-\Delta T &\approx& +37.5\degC
+3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot \degC}\cdot\Delta T \nonumber \\
+\Delta T &\approx& +37.5\degC \nonumber
 \eea
 Students are normally quite surprised at this number.  Although wildly unrealistic, $\Delta T \approx +6\degC$ is typically fatal, there is a related phenomena of diet-induced thermogenesis\cite{meat_sweats} known informally as ``the meat sweats''. Some students connect this calculation to feeling quite hungry after a cold swim in the pool (a similar effect).  On a larger scale, discussing what's wrong with this estimate is useful.  The main storage mechanism for storing food energy is fat tissue, which the calculation completely ignores.  Infants are generally born with little fat, and an infant sleeping through the night often coincides with the baby developing enough fat tissue to store sufficient kcals to make it though a night without waking up ravenously hungry.  A related follow-up is that if a person is stranded in the wilderness, they should immediately start walking downstream (ie, towards civilization) as they likely won't be able to harvest an amount of kcals equivalent to what they already have stored on their hips and abdomen.\cite{trout}  The contrast of bear hibernation \cite{fat_bear} and songbirds constantly eating through the winter are related connections to investigate.
 
@@ -103,9 +103,9 @@ The other $2$ blocks of energy are transformed into heat and leave the hiker's b
 	&=& 80kg\cdot10\frac{Joules}{kg\cdot m}\cdot height \label{eq:bar_chart}\\
 height &\approx&  1000 m
 \eea
-This estimate is again surprising to students.  Five trips up the bluff to burn off $\$2$ of saturated fat, sugar, and flour!  A nice followup calculation is to imagine a car that can burn a $100kcal$ piece of toast in the engine: from rest, what speed will the toast propel it to? If (again) the engine converts $1/3$ of the energy into motion (kinetic energy), a $1300kg$ Honda Civic will reach a speed of about $13\frac{m}{s}\approx33mph$!  
+This estimate is again surprising to students.  Five trips up the bluff to burn off $\$2$ of saturated fat, sugar, and flour!  A nice followup calculation is to imagine a car that can burn a $100kcal$ piece of toast in the engine: from rest, what speed will the toast propel it to? If (again) the engine converts $1/3$ of the energy into motion (kinetic energy), a $1300kg$ Honda Civic will reach a speed of about $15\frac{m}{s}\approx33mph$!  
 
-The point of these energy calculations is not to give students an eating disorder.  Rather, the numbers show food's amazing power. A single slice of toast will bring a car up to the residential speed limit!  A day's food, $3000kcal$, will power you up an $8000m$ mountain peak! The body-work food allows us to do is astonishing, and increases in food production have made modern  comforts, unimaginable $150$ years ago, possible to the point of being taken for granted.  
+The point of these energy calculations is not to give students an eating disorder.  Rather, the numbers show food's amazing power. A single slice of toast will bring a car up to the residential speed limit!  A day's food, $3000kcal$, will power you up an $5000m$ mountain peak! The body-work food allows us to do is astonishing, and increases in food production have made modern  comforts, unimaginable $150$ years ago, possible to the point of being taken for granted.  
 
 \clearpage
 
@@ -171,7 +171,7 @@ Unless the social model is one of a country Dacha or an endless suburb with no d
 %
 % https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjswtTZo8X8AhXkjokEHW-yD74QFnoECA8QAQ&url=http%3A%2F%2Fextension.agron.iastate.edu%2Forganicag%2Fresearchreports%2Fn-kltar98.pdf&usg=AOvVaw2mLZB25pv44LX_EBAR5kXU&cshid=1673638241316994
 %
-More emotionally charged conversations can be had about converting the United States to all organic agriculture, which, for corn, typically has a yield penalty of about $20-40bu/acre$ when compared to conventional production.  The 1917 data isn't directly applicable, but it relates. At $180bu/acre$ conventional corn requires $22~million~acres$ (half of Wisconsin, or all of Indiana) to feed the US population ($350$ million people) corn for a year.  The remainder of the corn belt can be devoted to animal feed, ethanol, and export.  If the corn belt was devoted to producing organic corn at lower yield \cite{organic_corn_yield}, we probably wouldn't starve, but cheap meat and ethanol vehicle fuel would likely disappear.   
+More emotionally charged conversations can be had about converting the United States to all organic agriculture, which, for corn, typically has a yield penalty of about $20-40bu/acre$ when compared to conventional production.  The 1917 data isn't directly applicable, but it relates. At $180bu/acre$ conventional corn requires $\approx 24~million~acres$ (half of Wisconsin, or all of Indiana) to feed the US population ($350$ million people) corn for a year.  The remainder of the corn belt can be devoted to animal feed, ethanol, and export.  If the corn belt was devoted to producing organic corn at lower yield \cite{organic_corn_yield}, we probably wouldn't starve, but cheap meat and ethanol vehicle fuel would likely disappear.   
 %WI 42M acres
 %IN 23M acres
 %
@@ -218,7 +218,7 @@ As the story goes, the two main commodity crops in Ireland were potatoes (for hu
 
 This inflammatory claim, which is certainly a simplified version of history, serves as a useful evaluation example for students. Specifically, in years that the potato crop failed because of weather or late blight, could the amount of oats produced (and exported) have fed the Irish population?  More broadly, was the Great Famine due to weather and disease, natural causes ``we can't do anything about,''  or was the depth of the tragedy a result of political choices?
 
-Some estimates follow:  Ireland's population in 1845 was about $8.5$ million people.  The island has an area of about $70,000km^2$ and you might estimate that $64\%$ of the land ($44,800km^2$) is arable for agriculture \cite{arable_percentage}.  
+Some estimates follow:  Ireland's population in 1845 was about $8.5$ million people.  The island has an area of about $84,400km^2$ \cite{IRE_area} and you might estimate that $64\%$ of the land ($54,000km^2$) is arable for agriculture \cite{arable_percentage}.  
 It seems reasonable to use the 1917 productivity,  figure \ref{1917_yields},  to make calculations for Ireland in 1845.  Reminder, in 1917, potatoes produced $1.908\times10^6 kcal/acre$ and oats $1.254\times10^6kcal/acre$.
 With students, evaluation of the claim could be approached as a series of questions:
 
@@ -242,7 +242,7 @@ How much land area, sown in oats, would produce this food?
  &\approx& 30,000 km^2 \nonumber
 \eea
 
-Summed, $49,700km^2$, these two farmland areas devoted to oats and potatoes only slightly exceed the amount of arable land estimated above for Ireland, $44,800km^2$ \cite{arable_percentage}.  What do the numbers mean?  Did there have to be a famine?  If all of the potato crop failed because of late blight, there would likely have been enough oats to feed the population a $2000kcal$ ration of oats with leftover to spare.  
+Summed, $49,700km^2$, these two areas devoted to oats and potatoes are roughly equivalent to the amount of arable land estimated above for Ireland, $54,000km^2$ \cite{arable_percentage}.  What do the numbers mean?  Did there have to be a famine?  If all of the potato crop failed because of late blight, there would likely have been enough oats to feed the population a $2000kcal$ ration of oats with leftover to spare.  
 Like the Holodomor or the Great Leap Forward, the numbers suggest that large-scale suffering wasn't  a natural disaster, but rather a human disaster resulting from poor government policy insensitive to the value of human life.    
 
 
@@ -353,7 +353,7 @@ Average USDA per acre yields for a number of commodity crops over time.  This ``
 
 ImageJ is a free software program developed by the National Institutes of Health for photo analysis, \cite{imageJ}.  I used the program to measure a calibration scale in a map and I also used the program to measure the area of two polygons that I drew on the map.  The length and both areas are shown in figure \ref{imageJ}.
 
-Specifically, to find the area of the two large chinampas areas near Tenochtitlan, I took a screenshot from the 1964 paper, \cite{Chinampas_1964}, and saved it in jpg format.  Then, I opened the image in the Windows-Java edition of ImageJ \cite{imageJ}.  The length of the 10 mile distance scale was 213 pixels. The long chinampas area at the south end of the lake was measured with a Polygon selection via the Mesure tool to have an area of $9940~pixel^2\approx21.9miles^2$.  The smaller region near Chalco had an area of about $1439~pixel^2\approx3.2miles^2$.  While there were certainly other regions devoted to chimanpas agriculture, the portion visible near the Aztec capital seems to be about $25.1miles^2$ or $16,000acres$.  
+Specifically, to find the area of the two large chinampas areas near Tenochtitlan, I took a screenshot from the 1964 paper, \cite{Chinampas_1964}, and saved it in jpg format.  Then, I opened the image in the Windows-Java edition of ImageJ \cite{imageJ}.  The length of the 10 mile distance scale was 213 pixels. The long chinampas area at the south end of the lake was measured with a Polygon selection via the Measure tool to have an area of $9940~pixel^2\approx21.9miles^2$.  The smaller region near Chalco had an area of about $1439~pixel^2\approx3.2miles^2$.  While there were certainly other regions devoted to chimanpas agriculture, the portion visible near the Aztec capital seems to be about $25.1miles^2$ or $16,000acres$.  
 
 \begin{figure}[ht!]
 \centering
@@ -649,6 +649,9 @@ The Little Ice Age: How Climate Made History 1300-1850
 Basic Books 
 2001.
 
+\bibitem{IRE_area}
+Currently, Northern Ireland and the Republic of Ireland are separate countries.  Together, their land area is about $84,400km^2$.
+
 \bibitem{Ireland_5M}
 Carroll R.
 Ireland’s population passes 5m for first time since C19th famine.